Čech cohomology of attractors of discrete dynamical systems

Let f:Rn→Rnf:Rn→Rn be a homeomorphism and K an asymptotically stable attractor for f. The aim of this paper is to study when the inclusion of K   in its basin of attraction A(K)A(K) induces isomorphisms in Čech cohomology. We show that (i) this is true if coefficients are taken in QQ or ZpZp (p prime) and (ii) it is true for integral cohomology if and only if the Čech cohomology of K   or A(K)A(K) is finitely generated. We compute the Čech cohomology of periodic point free attractors of volume-contracting R3R3-homeomorphisms and present applications to quite general models in population dynamics.